Generalized Cornfield conditions for the risk difference

TL;DR

This paper extends the classical Cornfield conditions to the risk difference and categorical confounders, providing more stringent thresholds and weaker assumptions, thereby enhancing sensitivity analysis in observational causal inference.

Contribution

It introduces generalized Cornfield conditions for the risk difference with categorical confounders, offering more precise thresholds and broader applicability.

Findings

New conditions for the risk difference extend classical results.

More stringent thresholds improve sensitivity analysis.

Applications demonstrate increased information over traditional conditions.

Abstract

A central question in causal inference with observational studies is the sensitivity of conclusions to unmeasured confounding. The classical Cornfield condition allows us to assess whether an unmeasured binary confounder can explain away the observed relative risk of the exposure on the outcome. It states that for an unmeasured confounder to explain away an observed relative risk, the association between the unmeasured confounder and the exposure, and also that between the unmeasured confounder and the outcome, must both be larger than the observed relative risk. In this paper, we extend the classical Cornfield condition in three directions. First, we consider analogous conditions for the risk difference, and allow for a categorical, not just a binary, unmeasured confounder. Second, we provide more stringent thresholds which the maximum of the above-mentioned associations must satisfy, rather than simply weaker conditions that both must satisfy. Third, we show that all previous results on Cornfield conditions hold under weaker assumptions than previously used. We illustrate their potential applications by real examples, where our new conditions give more information than the classical ones.